### Summary

You searched for: inst=-42

1

New Number: 2.20 |  AESZ: 133  |  Superseeker: 12 -3284/3  |  Hash: 4c9628f7dd48f4e9e6ec75303e557389

Degree: 2

$\theta^4-2^{2} 3 x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{4} 3^{3} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 8400, 44100, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -42, -3284/3, -20538, -103776, ... ; Common denominator:...

#### Discriminant

$1-144z+6912z^2$

#### Local exponents

$0$$\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I$$\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 3}{ 2}$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

Explicit solution not yet verified

2

New Number: 4.32 |  AESZ: 356  |  Superseeker: -14 -196  |  Hash: e73c971c3ed3a4fd581234510642c285

Degree: 4

$\theta^4-2 x\left(236\theta^4+472\theta^3+577\theta^2+341\theta+78\right)+2^{2} x^{2}\left(20836\theta^4+83344\theta^3+150531\theta^2+134374\theta+48664\right)-2^{6} 3 x^{3}\left(33984\theta^4+203904\theta^3+487828\theta^2+545916\theta+237757\right)+2^{10} 3^{2} x^{4}(12\theta+19)(12\theta+23)(12\theta+25)(12\theta+29)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 156, 21062, 2714208, 342489420, ...
--> OEIS
Normalized instanton numbers (n0=1): -14, -42, -196, -1218, -208446/5, ... ; Common denominator:...

#### Discriminant

$(128z-1)^2(108z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 128}$$\frac{ 1}{ 108}$$\infty$
$0$$0$$0$$\frac{ 19}{ 12}$
$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$\frac{ 23}{ 12}$
$0$$1$$1$$\frac{ 25}{ 12}$
$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 29}{ 12}$

#### Note:

3

New Number: 5.46 |  AESZ: 243  |  Superseeker: -42 -41706  |  Hash: 93c30005b5a976a2b7c5206d5e679a45

Degree: 5

$\theta^4+x\left(295\theta^4+572\theta^3+424\theta^2+138\theta+17\right)+2 x^{2}\left(843\theta^4+744\theta^3-473\theta^2-481\theta-101\right)+2 x^{3}\left(1129\theta^4-516\theta^3-725\theta^2-159\theta+4\right)-3 x^{4}\left(173\theta^4+352\theta^3+290\theta^2+114\theta+18\right)-3^{2} x^{5}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -17, 1549, -215585, 36505501, ...
--> OEIS
Normalized instanton numbers (n0=1): -42, 875, -41706, 2954224, -257813864, ... ; Common denominator:...

#### Discriminant

$-(z^3+57z^2-289z-1)(3z+1)^2$

#### Local exponents

≈$-61.684843$$-\frac{ 1}{ 3}$ ≈$-0.003458$$0$ ≈$4.688301$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$1$$1$$0$$1$$1$
$1$$3$$1$$0$$1$$1$
$2$$4$$2$$0$$2$$1$

#### Note:

A-incarnation: $7 \times 7$ linear Pfaffian in $P^7$.
There is a second MUM point at infinity, associated to
the 7 fold linear section of $G(2,7)$ AESZ 27/5.7